Subgroups — D₁₃⋊#1922 #16798763

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#424	C₂	1	1	yes	maximal, characteristic
2	#13131396	C₂	1	1	yes	maximal, characteristic
3	#13130904	C₂	1	2	yes	maximal, complemented
4	#13130903	C₂	1	2	yes	maximal, complemented
5	#13130902	C₂	1	2	yes	maximal, complemented
6	#13130901	C₂	1	2	yes	maximal, complemented
7	#13130528	C₂	1	1	yes	maximal, characteristic
8	#13130512	C₂	1	1	yes	maximal, characteristic
9	#13130512	C₂	1	1	yes	maximal, characteristic
10	C₂×(C₂×#261)⋊C₈	C₂	1	1	yes	maximal, characteristic
11	D₁₃×#427	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄×#261	C₂²	1	1	yes	characteristic
13	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
14	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
17	D₁₃×#117	C₂²	1	1	yes	characteristic
18	D₁₃×#117	C₂²	1	1	yes	characteristic
19	#11719079	C₂²	1	2	yes	—
20	#11719079	C₂²	1	2	yes	—
21	#11719072	C₂²	1	2	yes	—
22	#11719072	C₂²	1	2	yes	—
23	#11719067	—	2	2	no	—
24	#11719062	—	2	2	no	—
25	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
26	D₁₃⋊(C₄⋊C₈)	—	2	1	no	—
27	#11719047	—	2	1	no	—
28	C₄×D₁₃⋊C₈	—	2	1	no	—
29	C₁₃×#427	C₄	1	1	yes	characteristic, complemented
30	#11718767	C₄	1	1	yes	characteristic, complemented
31	#11718659	C₄	1	1	yes	characteristic, complemented
32	#11718659	C₄	1	1	yes	characteristic, complemented
33	#11718541	C₂²	1	1	yes	characteristic
34	#11718541	C₂²	1	1	yes	characteristic
35	D₁₃×#107	C₄	1	1	yes	characteristic, complemented
36	D₁₃×#107	C₄	1	1	yes	characteristic, complemented
37	#11718521	C₂²	1	1	yes	characteristic
38	#11718521	C₂²	1	1	yes	characteristic
39	D₁₃×#106	C₄	1	1	yes	characteristic, complemented
40	D₁₃×#106	C₄	1	1	yes	characteristic, complemented
41	#11718268	C₂²	1	2	yes	—
42	#11718268	C₂²	1	2	yes	—
43	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
44	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
45	#11718247	C₂²	1	2	yes	—
46	#11718247	C₂²	1	2	yes	—
47	#11718247	C₂²	1	2	yes	—
48	#11718247	C₂²	1	2	yes	—
49	C₂³×#261	—	2	1	no	—
50	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
51	C₂×#6122	—	2	1	no	—
52	C₂×#6122	—	2	1	no	—
53	C₂²×#1057	D₄	1	2	yes	—
54	C₂×C₄×#261	—	2	2	no	—
55	C₂×C₄×#261	—	2	2	no	—
56	C₂×C₄×#261	—	2	1	no	—
57	C₂×C₄×#261	C₂³	1	2	yes	—
58	D₁₃⋊M₁₆	—	2	2	no	—
59	D₁₃⋊M₁₆	—	2	2	no	—
60	D₁₃⋊M₁₆	—	2	2	no	—
61	D₁₃⋊M₁₆	Q₈	1	4	yes	—
62	C₂×#6118	C₂³	1	2	yes	—
63	C₂×#6118	C₂³	1	2	yes	—
64	C₂×D₁₃⋊C₈	—	2	1	no	—
65	C₂×D₁₃⋊C₈	—	2	2	no	—
66	C₂×D₁₃⋊C₈	—	2	2	no	—
67	C₂×D₁₃⋊C₈	—	2	1	no	—
68	C₂×D₁₃⋊C₈	D₄	1	1	yes	characteristic
69	C₂×D₁₃⋊C₈	D₄	1	1	yes	characteristic
70	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
73	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
74	#88180	C₂×C₄	1	1	yes	characteristic
75	#88180	C₂×C₄	1	1	yes	characteristic
76	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₁₃	—	2	2	no	—
78	C₂×C₈×D₁₃	—	2	2	no	—
79	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
83	#88146	C₂³	1	1	yes	characteristic
84	#88146	C₂³	1	1	yes	characteristic
85	#88146	C₂³	1	1	yes	characteristic
86	#88146	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊C₄×D₁₃	—	2	1	no	—
92	C₂²⋊C₄×D₁₃	—	2	1	no	—
93	#88131	—	2	1	no	—
94	#88131	—	2	1	no	—
95	#88126	—	2	1	no	—
96	#88126	—	2	1	no	—
97	C₄²×D₁₃	—	2	1	no	—
98	C₄²×D₁₃	—	2	1	no	—
99	#88112	—	2	2	no	—
100	#88112	—	2	2	no	—
101	#88110	—	2	2	no	—
102	#88110	—	2	2	no	—
103	C₄⋊#1057	—	2	2	no	—
104	C₄⋊#1057	—	2	2	no	—
105	C₄×#1057	—	2	2	no	—
106	C₄×#1057	—	2	2	no	—
107	C₁₃×#107	C₂×C₄	1	1	yes	characteristic, complemented
108	C₁₃×#107	C₂×C₄	1	1	yes	characteristic, complemented
109	C₁₃×#106	C₂×C₄	1	1	yes	characteristic, complemented
110	C₁₃×#106	C₂×C₄	1	1	yes	characteristic, complemented
111	#88058	C₂×C₄	1	1	yes	characteristic, complemented
112	#88058	C₂×C₄	1	1	yes	characteristic, complemented
113	#88057	C₂×C₄	1	1	yes	characteristic, complemented
114	#88057	C₂×C₄	1	1	yes	characteristic, complemented
115	#88048	C₂×C₄	1	1	yes	characteristic, complemented
116	#88048	C₂×C₄	1	1	yes	characteristic, complemented
117	#88048	C₂×C₄	1	1	yes	characteristic, complemented
118	#88048	C₂×C₄	1	1	yes	characteristic, complemented
119	#88047	C₂×C₄	1	1	yes	characteristic, complemented
120	#88047	C₂×C₄	1	1	yes	characteristic, complemented
121	#88047	C₂×C₄	1	1	yes	characteristic, complemented
122	#88047	C₂×C₄	1	1	yes	characteristic, complemented
123	C₂×#1922	—	13	1	no	maximal, Sylow
124	C₂³×D₁₃	#41	1	1	yes	characteristic
125	C₂²×#261	—	2	4	no	—
126	C₂²×#261	—	2	2	no	—
127	C₂²×#261	—	4	2	no	—
128	C₂²×#261	—	4	2	no	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×D₁₃	—	2	1	no	—
132	C₂×C₄×D₁₃	—	2	1	no	—
133	C₂×C₄×D₁₃	—	2	1	no	—
134	C₂×C₄×D₁₃	—	2	1	no	—
135	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
138	C₂×C₄×D₁₃	#41	1	2	yes	—
139	C₂×C₄×D₁₃	#41	1	2	yes	—
140	C₂×C₄×D₁₃	#41	1	2	yes	—
141	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
142	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
143	#6122	—	2	4	no	—
144	#6122	—	4	2	no	—
145	C₂×#1057	—	2	4	no	—
146	C₂×#1057	—	2	2	no	—
147	C₂×#1057	—	2	2	no	—
148	C₂×#1057	C₂×D₄	1	2	yes	—
149	C₂×#1057	C₂×D₄	1	2	yes	—
150	C₄×#261	—	2	2	no	—
151	C₄×#261	—	2	2	no	—
152	C₄×#261	—	4	2	no	—
153	#6118	—	2	2	no	—
154	#6118	—	2	2	no	—
155	#6118	—	2	2	no	—
156	#6118	C₂×Q₈	1	4	yes	—
157	D₁₃⋊C₈	—	2	4	no	—
158	D₁₃⋊C₈	—	2	2	no	—
159	D₁₃⋊C₈	—	2	2	no	—
160	D₁₃⋊C₈	—	2	2	no	—
161	D₁₃⋊C₈	—	2	2	no	—
162	D₁₃⋊C₈	—	4	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₂²⋊Dic₁₃	—	2	1	no	—
175	C₂²⋊Dic₁₃	—	2	1	no	—
176	#6103	—	2	1	no	—
177	#6103	—	2	1	no	—
178	#6103	—	2	1	no	—
179	#6103	—	2	1	no	—
180	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
184	#6101	—	2	1	no	—
185	#6101	—	2	1	no	—
186	#6101	—	2	1	no	—
187	#6101	—	2	1	no	—
188	C₄×Dic₁₃	—	2	1	no	—
189	C₄×Dic₁₃	—	2	1	no	—
190	C₄×Dic₁₃	—	2	1	no	—
191	C₄×Dic₁₃	—	2	1	no	—
192	C₄×Dic₁₃	—	2	1	no	—
193	C₄×Dic₁₃	—	2	1	no	—
194	C₂×#1055	—	2	2	no	—
195	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
196	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
197	C₈×D₁₃	—	2	2	no	—
198	C₈×D₁₃	—	2	2	no	—
199	C₈×D₁₃	—	2	1	no	—
200	C₈×D₁₃	—	2	1	no	—
201	C₈×D₁₃	—	2	1	no	—
202	C₈×D₁₃	—	2	1	no	—
203	C₂×#427	—	13	1	no	—
204	C₂×#424	—	13	1	no	—
205	C₂×#405	—	13	1	no	—
206	#1922	—	13	2	no	—
207	#1922	—	13	2	no	—
208	#1922	—	13	2	no	—
209	#1922	—	13	2	no	—
210	C₂×#341	—	13	1	no	—
211	C₂×#339	—	13	1	no	—
212	C₂×#339	—	13	1	no	—
213	C₂×#336	—	13	1	no	—
214	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
215	C₂²×D₁₃	—	2	2	no	—
216	C₂²×D₁₃	—	2	2	no	—
217	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
218	C₂²×D₁₃	#125	1	2	yes	—
219	C₂²×D₁₃	#126	1	2	yes	—
220	C₂²×D₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×#261	—	2	4	no	—
222	C₂×#261	—	4	2	no	—
223	C₂×#261	—	4	8	no	—
224	C₂×#261	—	4	2	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	#117	1	2	yes	—
230	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
232	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
233	C₂×Dic₁₃	—	2	1	no	—
234	C₂×Dic₁₃	—	2	1	no	—
235	C₂×Dic₁₃	—	2	1	no	—
236	C₂×Dic₁₃	—	2	1	no	—
237	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
238	C₂×Dic₁₃	C₂²⋊Q₈	1	2	yes	—
239	C₂×Dic₁₃	#123	1	2	yes	—
240	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₄×D₁₃	—	4	2	no	—
242	C₄×D₁₃	—	4	2	no	—
243	C₄×D₁₃	—	4	2	no	—
244	C₄×D₁₃	—	4	2	no	—
245	C₄×D₁₃	#117	1	2	yes	—
246	C₄×D₁₃	C₄×Q₈	1	2	yes	—
247	C₄×D₁₃	C₂²⋊Q₈	1	2	yes	—
248	C₄×D₁₃	#123	1	2	yes	—
249	C₄×D₁₃	#125	1	2	yes	—
250	C₄×D₁₃	#126	1	2	yes	—
251	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
252	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
253	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
254	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
255	#1057	—	2	4	no	—
256	#1057	—	2	2	no	—
257	#1057	—	2	2	no	—
258	#1057	—	4	2	no	—
259	C₈×C₁₃	—	2	1	no	—
260	C₈×C₁₃	—	2	1	no	—
261	#1055	—	2	1	no	—
262	#1055	—	2	1	no	—
263	C₂²×M₁₆	—	13	1	no	—
264	C₂²×M₁₆	—	13	1	no	—
265	C₂³×C₈	—	13	1	no	—
266	C₂³×C₈	—	13	1	no	—
267	C₂×#117	—	13	1	no	—
268	C₂×#117	—	13	1	no	—
269	C₂²×C₄²	—	13	1	no	—
270	#427	—	13	1	no	—
271	#427	—	13	1	no	—
272	#427	—	13	1	no	—
273	#427	—	13	1	no	—
274	#427	—	13	1	no	—
275	#427	—	13	1	no	—
276	#427	—	13	1	no	—
277	#427	#261	1	1	yes	characteristic, complemented
278	C₂×#107	—	13	1	no	—
279	C₂×#107	—	13	1	no	—
280	C₂×#106	—	13	1	no	—
281	C₂×#106	—	13	1	no	—
282	#424	—	13	2	no	—
283	#424	—	13	2	no	—
284	#424	—	26	2	no	—
285	C₂×C₄⋊C₈	—	26	1	no	—
286	C₂×C₄⋊C₈	—	26	1	no	—
287	#405	—	13	2	no	—
288	#405	—	13	2	no	—
289	#405	—	26	2	no	—
290	C₂×#97	—	26	1	no	—
291	C₂×C₄×C₈	—	26	1	no	—
292	#341	—	13	2	no	—
293	#341	—	13	2	no	—
294	#339	—	13	2	no	—
295	#339	—	13	2	no	—
296	#339	—	13	2	no	—
297	#339	—	13	2	no	—
298	#336	—	13	2	no	—
299	#336	—	13	2	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	#387	1	2	yes	—
303	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂×D₁₃	—	2	1	no	—
305	C₂×D₁₃	—	2	1	no	—
306	C₂×D₁₃	—	2	4	no	—
307	C₂×D₁₃	—	2	4	no	—
308	C₂×D₁₃	#387	1	2	yes	—
309	C₂×D₁₃	#443	1	2	yes	—
310	C₂×D₁₃	#444	1	2	yes	—
311	C₂×D₁₃	C₂×#125	1	1	yes	characteristic
312	C₂×D₁₃	C₂×#126	1	1	yes	characteristic
313	#261	—	4	4	no	—
314	C₄×C₁₃	—	4	1	no	—
315	C₄×C₁₃	—	4	1	no	—
316	C₄×C₁₃	—	4	1	no	—
317	C₄×C₁₃	—	4	1	no	—
318	C₄×C₁₃	#387	1	2	yes	—
319	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
320	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
321	Dic₁₃	—	4	1	no	—
322	Dic₁₃	—	4	1	no	—
323	Dic₁₃	—	4	1	no	—
324	Dic₁₃	—	4	1	no	—
325	Dic₁₃	#387	1	2	yes	—
326	Dic₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
327	Dic₁₃	C₂×#123	1	1	yes	characteristic
328	C₂³×C₄	—	13	1	no	—
329	C₂³×C₄	—	26	1	no	—
330	C₂×M₁₆	—	13	2	no	—
331	C₂×M₁₆	—	13	4	no	—
332	C₂×M₁₆	—	13	2	no	—
333	C₂×M₁₆	—	26	1	no	—
334	C₂×M₁₆	—	26	2	no	—
335	C₂×M₁₆	—	26	1	no	—
336	C₂×M₁₆	—	26	2	no	—
337	C₂×M₁₆	—	26	2	no	—
338	C₂²×C₈	—	13	2	no	—
339	C₂²×C₈	—	13	1	no	—
340	C₂²×C₈	—	13	1	no	—
341	C₂²×C₈	—	13	2	no	—
342	C₂²×C₈	—	13	1	no	—
343	C₂²×C₈	—	13	1	no	—
344	C₂²×C₈	—	13	1	no	—
345	C₂²×C₈	—	13	1	no	—
346	C₂²×C₈	—	13	1	no	—
347	C₂²×C₈	—	26	2	no	—
348	C₂²×C₈	—	26	2	no	—
349	C₂²×C₈	—	26	2	no	—
350	C₂²×C₈	—	26	2	no	—
351	C₂²×C₈	—	26	1	no	—
352	C₂²×C₈	—	26	1	no	—
353	C₂²×C₈	C₂×#261	1	1	yes	characteristic
354	#117	—	13	1	no	—
355	#117	—	13	1	no	—
356	#117	—	13	1	no	—
357	#117	—	13	1	no	—
358	#117	—	13	1	no	—
359	#117	—	13	1	no	—
360	#117	—	26	1	no	—
361	#117	—	26	1	no	—
362	#117	—	26	1	no	—
363	#117	—	26	1	no	—
364	#117	C₂×#261	1	1	yes	characteristic
365	#117	C₂×#261	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	13	1	no	—
367	C₂×C₄⋊C₄	—	13	1	no	—
368	C₂×C₄⋊C₄	—	13	1	no	—
369	C₂×C₄⋊C₄	—	13	1	no	—
370	C₂×C₂²⋊C₄	—	26	1	no	—
371	C₂×C₂²⋊C₄	—	26	1	no	—
372	C₂×C₄²	—	13	2	no	—
373	C₂×C₄²	—	26	1	no	—
374	C₂×C₄²	—	26	1	no	—
375	C₂×C₄²	—	26	2	no	—
376	C₂×C₄²	—	26	2	no	—
377	C₂×C₄²	—	26	1	no	—
378	#107	—	13	1	no	—
379	#107	—	13	1	no	—
380	#107	—	13	1	no	—
381	#107	—	13	1	no	—
382	#107	—	13	1	no	—
383	#107	—	13	1	no	—
384	#107	C₂×#261	1	1	yes	characteristic, complemented
385	#107	C₂×#261	1	1	yes	characteristic, complemented
386	#106	—	13	1	no	—
387	#106	—	13	1	no	—
388	#106	—	13	1	no	—
389	#106	—	13	1	no	—
390	#106	—	13	1	no	—
391	#106	—	13	1	no	—
392	#106	C₂×#261	1	1	yes	characteristic, complemented
393	#106	C₂×#261	1	1	yes	characteristic, complemented
394	C₄⋊C₈	—	26	2	no	—
395	C₄⋊C₈	—	26	2	no	—
396	C₄⋊C₈	—	26	2	no	—
397	C₄⋊C₈	—	26	2	no	—
398	#97	—	26	2	no	—
399	#97	—	26	2	no	—
400	C₄×C₈	—	26	2	no	—
401	C₄×C₈	—	26	2	no	—
402	C₂×C₁₃	—	2	2	no	—
403	C₂×C₁₃	C₂×#387	1	1	yes	characteristic
404	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
405	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
406	D₁₃	—	2	1	no	—
407	D₁₃	—	2	1	no	—
408	D₁₃	#1922	1	4	yes	complemented
409	C₂⁴	—	13	1	no	—
410	C₂²×C₄	—	13	1	no	—
411	C₂²×C₄	—	13	2	no	—
412	C₂²×C₄	—	13	2	no	—
413	C₂²×C₄	—	13	1	no	—
414	C₂²×C₄	—	13	1	no	—
415	C₂²×C₄	—	13	2	no	—
416	C₂²×C₄	—	13	2	no	—
417	C₂²×C₄	—	13	1	no	—
418	C₂²×C₄	—	13	1	no	—
419	C₂²×C₄	—	26	1	no	—
420	C₂²×C₄	—	26	1	no	—
421	C₂²×C₄	—	26	1	no	—
422	C₂²×C₄	—	26	1	no	—
423	C₂²×C₄	—	26	2	no	—
424	C₂²×C₄	—	26	4	no	—
425	C₂²×C₄	—	52	2	no	—
426	C₂²×C₄	—	52	2	no	—
427	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
428	M₁₆	—	13	4	no	—
429	M₁₆	—	26	2	no	—
430	M₁₆	—	26	4	no	—
431	M₁₆	—	26	2	no	—
432	M₁₆	—	26	2	no	—
433	M₁₆	—	52	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	13	2	no	—
436	C₂×C₈	—	13	2	no	—
437	C₂×C₈	—	13	1	no	—
438	C₂×C₈	—	13	1	no	—
439	C₂×C₈	—	26	1	no	—
440	C₂×C₈	—	26	1	no	—
441	C₂×C₈	—	26	1	no	—
442	C₂×C₈	—	26	1	no	—
443	C₂×C₈	—	26	2	no	—
444	C₂×C₈	—	26	2	no	—
445	C₂×C₈	—	26	2	no	—
446	C₂×C₈	—	26	2	no	—
447	C₂×C₈	—	26	2	no	—
448	C₂×C₈	—	26	2	no	—
449	C₂×C₈	—	26	2	no	—
450	C₂×C₈	—	26	4	no	—
451	C₂×C₈	—	26	4	no	—
452	C₂×C₈	—	26	2	no	—
453	C₂×C₈	—	26	2	no	—
454	C₂×C₈	—	52	2	no	—
455	C₂×C₈	C₂²×#261	1	1	yes	characteristic
456	C₂×C₈	C₂²×#261	1	1	yes	characteristic
457	C₄⋊C₄	—	13	1	no	—
458	C₄⋊C₄	—	13	1	no	—
459	C₄⋊C₄	—	13	1	no	—
460	C₄⋊C₄	—	13	1	no	—
461	C₄⋊C₄	—	26	1	no	—
462	C₄⋊C₄	—	26	1	no	—
463	C₄⋊C₄	—	26	1	no	—
464	C₄⋊C₄	—	26	1	no	—
465	C₄⋊C₄	C₂²×#261	1	1	yes	characteristic
466	C₄⋊C₄	C₂²×#261	1	1	yes	characteristic
467	C₄⋊C₄	C₂²×#261	1	1	yes	characteristic
468	C₄⋊C₄	C₂²×#261	1	1	yes	characteristic
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	26	1	no	—
472	C₂²⋊C₄	—	26	1	no	—
473	C₂²⋊C₄	—	26	1	no	—
474	C₂²⋊C₄	—	26	1	no	—
475	C₂²⋊C₄	—	26	1	no	—
476	C₂²⋊C₄	—	26	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	26	1	no	—
480	C₄²	—	26	1	no	—
481	C₄²	—	26	1	no	—
482	C₄²	—	26	1	no	—
483	C₄²	—	26	2	no	—
484	C₄²	—	26	2	no	—
485	C₄²	—	26	1	no	—
486	C₄²	—	26	1	no	—
487	C₄²	—	52	2	no	—
488	C₁₃	C₂×#1922	1	1	yes	characteristic, complemented, Sylow
489	C₂³	—	13	1	no	—
490	C₂³	—	13	2	no	—
491	C₂³	—	13	2	no	—
492	C₂³	—	13	1	no	—
493	C₂³	—	26	2	no	—
494	C₂³	—	26	2	no	—
495	C₂³	D₄×#261	1	1	yes	characteristic
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	13	2	no	—
501	C₂×C₄	—	13	2	no	—
502	C₂×C₄	—	13	1	no	—
503	C₂×C₄	—	13	1	no	—
504	C₂×C₄	—	13	2	no	—
505	C₂×C₄	—	13	2	no	—
506	C₂×C₄	—	13	2	no	—
507	C₂×C₄	—	13	2	no	—
508	C₂×C₄	—	13	1	no	—
509	C₂×C₄	—	13	1	no	—
510	C₂×C₄	—	13	2	no	—
511	C₂×C₄	—	13	1	no	—
512	C₂×C₄	—	13	1	no	—
513	C₂×C₄	—	13	2	no	—
514	C₂×C₄	—	26	4	no	—
515	C₂×C₄	—	26	1	no	—
516	C₂×C₄	—	26	1	no	—
517	C₂×C₄	—	26	1	no	—
518	C₂×C₄	—	26	1	no	—
519	C₂×C₄	—	52	2	no	—
520	C₂×C₄	—	52	2	no	—
521	C₂×C₄	—	52	2	no	—
522	C₂×C₄	—	52	2	no	—
523	C₂×C₄	—	52	2	no	—
524	C₂×C₄	—	52	8	no	—
525	C₂×C₄	—	52	2	no	—
526	C₂×C₄	#88237	1	2	yes	—
527	C₂×C₄	D₄×#261	1	1	yes	characteristic
528	C₂×C₄	Q₈×#261	1	2	yes	—
529	C₂×C₄	C₂³×#261	1	1	yes	characteristic
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	26	2	no	—
533	C₈	—	26	2	no	—
534	C₈	—	26	4	no	—
535	C₈	—	26	1	no	—
536	C₈	—	26	1	no	—
537	C₈	—	52	2	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	13	2	no	—
541	C₂²	—	13	2	no	—
542	C₂²	—	13	2	no	—
543	C₂²	—	13	1	no	—
544	C₂²	—	13	1	no	—
545	C₂²	—	26	4	no	—
546	C₂²	—	26	4	no	—
547	C₂²	—	26	1	no	—
548	C₂²	—	26	1	no	—
549	C₂²	#11719082	1	2	yes	—
550	C₂²	C₂×D₄×#261	1	1	yes	characteristic
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	13	1	no	—
556	C₄	—	13	1	no	—
557	C₄	—	13	2	no	—
558	C₄	—	52	4	no	—
559	C₄	—	52	1	no	—
560	C₄	—	52	1	no	—
561	C₄	—	52	1	no	—
562	C₄	—	52	1	no	—
563	C₄	#11719082	1	2	yes	—
564	C₄	C₂×#88237	1	1	yes	characteristic
565	C₄	C₂×Q₈×#261	1	1	yes	characteristic
566	C₂	—	2	2	no	—
567	C₂	—	13	4	no	—
568	C₂	—	26	1	no	—
569	C₂	—	26	1	no	—
570	C₂	C₂×#11719082	1	1	yes	characteristic
571	C₂	D₁₃⋊#443	1	1	yes	characteristic
572	C₂	D₁₃⋊#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#427	C₄
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#427	#261
hypocenter	C₁₃	C₂×#1922
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #13130904	C₂	semidirect
4. #13130903	C₂	semidirect
5. #13130902	C₂	semidirect
6. #13130901	C₂	semidirect
29. C₁₃×#427	C₄	semidirect
30. #11718767	C₄	semidirect
31. #11718659	C₄	semidirect
32. #11718659	C₄	semidirect
35. D₁₃×#107	C₄	semidirect
36. D₁₃×#107	C₄	semidirect
39. D₁₃×#106	C₄	semidirect
40. D₁₃×#106	C₄	semidirect
107. C₁₃×#107	C₂×C₄	semidirect
108. C₁₃×#107	C₂×C₄	semidirect
109. C₁₃×#106	C₂×C₄	semidirect
110. C₁₃×#106	C₂×C₄	semidirect
111. #88058	C₂×C₄	semidirect
112. #88058	C₂×C₄	semidirect
113. #88057	C₂×C₄	semidirect
114. #88057	C₂×C₄	semidirect
115. #88048	C₂×C₄	semidirect
116. #88048	C₂×C₄	semidirect
117. #88048	C₂×C₄	semidirect
118. #88048	C₂×C₄	semidirect
119. #88047	C₂×C₄	semidirect
120. #88047	C₂×C₄	semidirect
121. #88047	C₂×C₄	semidirect
122. #88047	C₂×C₄	semidirect
277. #427	#261	semidirect
384. #107	C₂×#261	semidirect
385. #107	C₂×#261	semidirect
392. #106	C₂×#261	semidirect
393. #106	C₂×#261	semidirect
408. D₁₃	#1922	semidirect
488. C₁₃	C₂×#1922	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₃⋊#424	2
#13131396	2
#13130904	2
#13130903	2
#13130902	2
#13130901	2
#13130528	2
#13130512	2
C₂×(C₂×#261)⋊C₈	2
D₁₃×#427	2
C₂×#1922	13

Subgroups — D13⋊#1922 #16798763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#1922 #16798763